Resumen de Error estimates for lie transformations

Jesús Francisco Palacián Subiela, Patricia Yanguas Sayas

• Lie transformations are commonly used to simplify dynamical systems through asymptotic changes of variables in such a way that the main qualitative features of the original system are preserved. For instance, by means of the analysis of the transformed system one can obtain explicit expressions of periodic orbits or invariant tori of the original one. These transformations are not convergent, in general; nevertheless it is possible to calculate upper bounds of the error of the truncation. What we propose here is an easy but effective way to make an estimation of this error. The central idea is to compose the inverse and direct transformations. In order to illustrate our procedure, some examples of applications to dissipative, as well as Hamiltonian systems, are shown.